Let's say the NP complete problem A can be solved in O(f(n)), where n is the problem size. And B can be solved in O(g(n)), where g is much larger than f. If we reduce an instance of B to an instance of A, the problem size is very unlikely to stay unchanged. Lets say the problem size is changed from n to h(n), and the time used for the reduction is negligible.
Then solving he instance of B by reducing it to an instance of A will take O (f(h(n))), which may very well be a lot larger than O(g(n)). For example, if both A and B can be solved in O(c^n) for different fixed c > 1, and the reduction changes the instance size from n to n^2, then the reduction will result in a much slower solution.
So your assumption is completely wrong. 1.27^3 > 2, so if you have a problem that can be solved in O(2^n), and you use a reduction to your O(1.27^n) problem that increases the instance size just by a factor 3, the reduction leads to a slower algorithm.